Sudoku: From Number Place to the World

An American pencil puzzle

The puzzle most people now call sudoku is generally credited to Howard Garns. It first appeared in 1979 in Dell Pencil Puzzles and Word Games, under the name "Number Place". The grid is 9 by 9, and the rule is short: every row, every column and every 3 × 3 box must contain the digits 1 to 9, each exactly once.

It did not begin as a headline. It sat among crosswords and other pencil puzzles, the kind people solve with a pencil and an eraser, one square at a time.

Japan gives it a name

In 1984 the Japanese publisher Nikoli, known for its puzzle magazines, introduced the puzzle to its readers and named it sudoku. From there the puzzle began to travel.

The Times and the world

The puzzle spread worldwide after The Times in London began printing it in 2004. Newspapers and puzzle books in many countries followed, and the grid became familiar to solvers across the world.

Why a good puzzle has one answer

A well-made sudoku has exactly one solution. That matters because every move can be justified by logic rather than luck. If a puzzle had two possible answers, a solver who reached a tricky point would have to guess, and the satisfaction of working out the next square would be lost.

Here is a simple way to see it. Suppose a row already has eight digits filled in. The one digit left must go in the one empty square, so no guessing is needed. Puzzle makers remove clues only while the answer stays unique, which is why a well-made puzzle can be solved step by step.

Tip: when you reach a dead end, look at the row, column and box you filled most recently. A repeated digit there usually points to the mistake.

A 4 × 4 walk-through

A 4 × 4 grid is a good place to practise. Work through it in three kinds of pass:

1. Find any row, column or box with only one empty square. The missing digit is whichever digit the other three squares lack.
2. Where a square could hold several digits, pencil in the small candidates so you can see them.
3. Look for a digit that fits in only one square of a row, column or box, and place it there.

Repeat until the grid is full. If you get stuck, check your earlier placements, because one wrong digit often causes every later dead end.

Erase candidates as soon as you rule them out, and keep your pencil marks small so the grid stays readable. Many solvers find that the first real breakthrough is a digit that can go in only one square of a row. Once you spot one, the puzzle tends to open up, and several more digits can follow.

Simpler versions for beginners and children

Sudoku scales down well. Two smaller sizes suit beginners and children:

• 4 × 4: digits 1 to 4, with 2 × 2 boxes. It takes minutes to finish and teaches the three rules: each row, column and box holds every digit once.
• 6 × 6: digits 1 to 6, with boxes two rows high and three columns wide. The boxes are no longer square, but the logic is the same, so it is a comfortable next step.

Start with a grid where about half the squares are filled in. Ask the child why each new digit must go where it does. That explanation is often where the learning happens.

Paperoom's sudoku maker prints puzzles with answer keys, so you can check a child's work without a second book. Before you print a full set, print one test sheet at 100 per cent scale with browser headers and footers turned off, so the boxes come out the right size. Choose A4 or US Letter to match the paper in your printer.

If your player enjoys the logic but wants a picture at the end, try a nonogram. Nonograms were devised in Japan in the late 1980s, and they are solved with similar row-and-column reasoning. The numbers beside each row and column give the lengths of the filled runs, and the picture appears as you work.